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Self-calibration of a 1D projective camera and its application to the self-calibration of a 2D projective camera

Part of the Lecture Notes in Computer Science book series (LNCS,volume 1406)

Abstract

We introduce the concept of self-calibration of a 1D projective camera from point correspondences, and describe a method for uniquely determining the two internal parameters of a 1D camera based on the trifocal tensor of three 1D images. The method requires the estimation of the trifocal tensor which can be achieved linearly with no approximation unlike the trifocal tensor of 2D images, and solving for the roots of a cubic polynomial in one variable. Interestingly enough, we prove that a 2D camera undergoing a planar motion reduces to a 1D camera. From this observation, we deduce a new method for self-calibrating a 2D camera using planar motions.

Both the self-calibration method for a 1D camera and its applications for 2D camera calibration are demonstrated on real image sequences. Other applications including 2D affine camera self-calibration are also discussed.

Keywords

  • Planar Motion
  • Internal Parameter
  • Optical Center
  • Principal Point
  • Point Correspondence

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. M. Armstrong, A. Zisserman, and R. Hartley. Self-calibration from image triplets. ECCV, 3–16, 1996.

    Google Scholar 

  2. M. Armstrong. Self-calibration from image sequences. Ph.D. Thesis, University of Oxford, 1996.

    Google Scholar 

  3. P.A. Beardsley and A. Zisserman. Affine calibration of mobile vehicles. Europe-China Workshop on GMICV, 214–221. 1995.

    Google Scholar 

  4. T. Buchanan. The twisted cubic and camera calibration. CVGIP, 42(1):130–132, 1988.

    MATH  MathSciNet  Google Scholar 

  5. O. Faugeras. Stratification of three-dimensional vision: Projective, affine and metric representations. JOSA, 12:465–484, 1995.

    Google Scholar 

  6. O. Faugeras and S. Maybank. Motion from point matches: Multiplicity of solutions. IJCV, 3(4):225–246, 1990.

    CrossRef  Google Scholar 

  7. O. Faugeras and B. Mourrain. About the correspondences of points between n images. Workshop on Representation of Visual Scenes, 37–44, 1995.

    Google Scholar 

  8. R. Hartley. In defence of the 8-point algorithm. ICCV, 1064–1070, 1995.

    Google Scholar 

  9. R.I. Hartley. A linear method for reconstruction from lines and points. ICCV, 882–887, 1995.

    Google Scholar 

  10. A. Heyden. Geometry and Algebra of Multiple Projective Transformations. Ph.D. thesis, Lund University, 1995.

    Google Scholar 

  11. Q.-T. Luong and O. Faugeras. Self-calibration of a moving camera from point correspondences and fundamental matrices. IJCV, 22(3):261–289, 1997.

    CrossRef  Google Scholar 

  12. S.J. Maybank and O.D. Faugeras. A theory of self calibration of a moving camera. IJCV, 8(2):123–151, 1992.

    CrossRef  Google Scholar 

  13. R. Mohr, B. Boufama, and P. Brand. Understanding positioning from multiple images. AI, (78):213–238, 1995.

    Google Scholar 

  14. L. Quan. Uncalibrated 1D projective camera and 3D affine reconstruction of lines. CVPR, 60–65, 1997.

    Google Scholar 

  15. L. Quan and T. Kanade. Affine structure from line correspondences with uncalibrated affine cameras. Trans. PAMI, 19(8):834–845, 1997.

    Google Scholar 

  16. L. Quan. Algebraic Relations among Matching Constraints of Multiple Images. Technical Report INRIA, RR-3345, Jan. 1998 (also TR Lifia-Imag 1995).

    Google Scholar 

  17. A. Shashua. Algebraic functions for recognition. Trans. PAMI, 17(8):779–789, 1995.

    Google Scholar 

  18. M. Spetsakis and J. Aloimonos. A unified theory of structure from motion. DARPA Image Understanding Workshop, 271–283, 1990.

    Google Scholar 

  19. P. Sturm. Vision 3D non calibrée: contributions à la reconstruction projective et étude des mouvements critiques pour l'auto-calibrage. Ph.D. Thesis, INPG, 1997.

    Google Scholar 

  20. P.H.S. Torr and A. Zissermann. Performance characterization of fundamental matrix estimation under image degradation. MVA, 9:321–333, 1997.

    Google Scholar 

  21. B. Triggs. Matching constraints and the joint image. ICCV, 338–343, 1995.

    Google Scholar 

  22. Cyril Zeller and Olivier Faugeras. Camera self-calibration from video sequences: the Kruppa equations revisited. Research Report 2793, INRIA, February 1996.

    Google Scholar 

  23. Z. Zhang, R. Deriche, O. Faugeras, and Q.T. Luong. A robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry. AI, 78:87–119, 1995.

    Google Scholar 

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© 1998 Springer-Verlag Berlin Heidelberg

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Faugeras, O., Quan, L., Sturm, P. (1998). Self-calibration of a 1D projective camera and its application to the self-calibration of a 2D projective camera. In: Burkhardt, H., Neumann, B. (eds) Computer Vision — ECCV'98. ECCV 1998. Lecture Notes in Computer Science, vol 1406. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0055658

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  • DOI: https://doi.org/10.1007/BFb0055658

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64569-6

  • Online ISBN: 978-3-540-69354-3

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